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In this dramatic image, we witness two rather chunky pixelated letter X's (having recently fattened themselves up for the approaching winter) locked in mortal combat, fighting to the death for the right to claim territory and ultimately to survive and have offspring.* It may seem cruel, but it is nature's way.

Two chunky pixelated letter X's fighting to the death!

But of course none of this actually matters to this puzzle. What does matter is that the above shape can be wrapped onto the surface of a cube in a way that perfectly covers the entire cube, with no gaps and no overlaps. Your task is to show how this can be done.


*You might need to, um, squint with your brain a bit in order to see this.

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    $\begingroup$ I know how. I just don’t have the tech skills to show that I know :p $\endgroup$
    – Earlien
    Aug 10, 2020 at 0:44

3 Answers 3

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As I don't have a camera handy, I have had to unfold my (pink) cube before I could show it to you. Its sides are $\sqrt{52} = \sqrt{4^2+6^2}$ units long.

enter image description here

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    $\begingroup$ Ninja! (...spoiler tag, please) $\endgroup$
    – Daniel Mathias
    Aug 10, 2020 at 1:29
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    $\begingroup$ This answer seems incomplete to me. Sure, I can think up which piece outside the pink area ends up where, but shouldn't that be a part of this answer? $\endgroup$
    – Jasper
    Aug 10, 2020 at 9:55
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    $\begingroup$ The answer requires a bit of mental visualization on the part of the viewer, but it's not incomplete. Assuming we don't cut things up, and the black sheet is directly under the pink sheet, there's only one way the pink sheet can fold up into a cube, and there's only one way the black bits can fold up around that. Any part of the black shape that goes past an edge is simply folded over that edge. Any point of black and pink that are currently touching will (must) remain touching. $\endgroup$
    – GrandOpener
    Aug 10, 2020 at 21:32
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    $\begingroup$ @GrandOpener I disagree. If this happened to be wrong because some part didn't fit (and there was some other solution that was right - which is of course unlikely, but bear with me for a moment) if you used just this answer, you'd probably miss that. That makes it an incomplete answer. It points in the direction of the answer, but doesn't actually show that it's right, and leaves that up to the reader. $\endgroup$
    – Jasper
    Aug 11, 2020 at 6:18
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    $\begingroup$ @GrandOpener But isn't an answer for all visitors of this site, rather than some transaction between the asker and the answerer? $\endgroup$
    – Jasper
    Aug 11, 2020 at 22:06
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The combined area of the X's is

312 square units. This means each face of the cube must have an area of 52 square units. The edge length of the cube is then the square root of 52 units, which is the length of the hypotenuse of a right triangle with legs of length 4 and 6 units.

The solution:

enter image description here

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    $\begingroup$ I like this answer better. This answer shows how the X's can be folded onto the surface of the cube completely covering the face of it. I also love the math explanation but the graph paper drawing is what really makes it clear. After a long comparison with the accepted answer I do see it, but just saying this one is clearer to ME. :) $\endgroup$
    – PRS
    Aug 10, 2020 at 8:30
  • $\begingroup$ I feel this is the better answer, too. $\endgroup$
    – justhalf
    Aug 12, 2020 at 1:41
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Here's a diagram showing both the parts of the shape that make up each face of the cube in its own colour, and trying to give some indication of how they meet up when folded.

Coloured diagram showing the shape broken up as a net of a cube

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  • $\begingroup$ What software did you use to make this? $\endgroup$
    – Toby Mak
    Aug 11, 2020 at 7:05
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    $\begingroup$ I used Inkscape. The font is Exo. The pieces were drawn and copied on a square grid and then rotated back to the orientation from the puzzle. $\endgroup$
    – Weeble
    Aug 11, 2020 at 13:36

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